To prepare the aioli: At least 2 hours before serving. Mix together ½ cup of mayonnaise, ⅓ cup of chili sauce, 1 teaspoon creole mustard, ½ teaspoon creole seasoning, ½ teaspoon lemon juice and one minced garlic clove. Chill until serving.
To make the squash cakes: Grate the zucchini and yellow squash, then ring in paper towels or a kitchen towel to remove any excess moisture. Add to a medium mixing bowl with the remaining ingredients.
Use a spoon or large spatula and mix until the mixture comes together and is fully combined. The dry cracker crumbs will help to soak up any residual moisture and the eggs and grated Parmesan will bind the mixture.
On the stove top in a large skillet, heat around 4 tablespoons of olive oil over medium-high heat in a sauce pan. A few additional drizzles of olive oil will need to be added to the pan between frying the squash cake.
Use a 4 ounce ice cream scoop to divide the squash mixture and scoop into the pan. Don't attempt to flatten the squash cakes until you turn them, the batter is sticky and it will only stick to the spatula. Cook for 3-4 minutes, then turn.
Flatten to about ¾ inches thick, then cook on the other side for another 4 minutes or until cooked through. The cakes should be golden and crispy. Remove to a paper towel to drain any excess oil.
Serve hot with a side of creamy Cajun aioli.